CELEBRATING 30 YEARS
http://dx.doi.org/10.1287/mksc.1110.0656
© 2011 INFORMS
Vol. 30, No. 5, September–October 2011, pp. 757–775
issn 0732-2399 — eissn 1526-548X — 11 — 3005 — 0757
Firm Strategies in the “Mid Tail” of
Platform-Based Retailing
Baojun Jiang
Olin Business School, Washington University in St. Louis, St. Louis, Missouri 63130, [email protected]
Kinshuk Jerath, Kannan Srinivasan
Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
{[email protected], [email protected]}
W
hile millions of products are sold on its retail platform, Amazon.com itself stocks and sells only a very
small fraction of them. Most of these products are sold by third-party sellers who pay Amazon a fee
for each unit sold. Empirical evidence clearly suggests that Amazon tends to sell high-demand products and
leave long-tail products for independent sellers to offer. We investigate how a platform owner such as Amazon,
facing ex ante demand uncertainty, may strategically learn from these sellers’ early sales which of the “mid-tail”
products are worthwhile for its direct selling and which are best left for others to sell. The platform owner’s
“cherry-picking” of the successful products, however, gives an independent seller the incentive to mask any
high demand by lowering his sales with a reduced service level (unobserved by the platform owner).
We analyze this strategic interaction between a platform owner and an independent seller using a gametheoretic model with two types of sellers—one with high demand and one with low demand. We show that it
may not always be optimal for the platform owner to identify the seller’s demand. Interestingly, the platform
owner may be worse off by retaining its option to sell the independent seller’s product, whereas both types of
sellers may benefit from the platform owner’s threat of entry. The platform owner’s entry option may reduce
consumer surplus in the early period, although it increases consumer surplus in the later period. We also
investigate how consumer reviews influence the market outcome.
Key words: platform; retailing; long-tail products; signaling; asymmetric information; pooling equilibrium
History: Received: June 21, 2010; accepted: April 2, 2011; Eric Bradlow served as the editor-in-chief and Duncan
Simester served as associate editor for this article. Published online in Articles in Advance July 15, 2011.
1.
Introduction
products are sold by third-party sellers. For instance,
Amazon directly sells only 7% of the products in its
electronics category, and the remaining 93% are sold
by independent sellers. The second column of Table 1
shows a similar sales pattern for various other product categories. Third-party sellers can list their products on Amazon.com, which displays these listings to
a consumer whenever she conducts a related search.1
For every unit sold, Amazon charges the seller a fee.
In this manner, the third-party sellers benefit from
access to the tens of millions of consumers on Amazon.com. In turn, Amazon benefits from these sellers’
sales, and the increased product variety helps Amazon attract and retain more online customers. Because
of these symbiotic advantages, an increasing number
of large retailers are establishing similar online retail
platforms. For example, Sears has recently launched
“Marketplace at Sears.com” to facilitate sales by
independent sellers. Clearly, third-party selling on
Amazon.com, as a dominant platform-based retailer,
not only sells products directly but also allows hundreds of thousands of third-party sellers (also known
as independent sellers) to sell products on its retail
platform. Consequently, it offers a spectacular range
and variety; e.g., it lists for sale over two million products in the “electronics” category alone. The product
variety available on Amazon dwarfs what is available at Walmart, the largest traditional (nonplatform)
retailer, by several orders of magnitude. For example, during April 2010, a staggering 8,010 digital camera products were listed for sale on Amazon, whereas
408 such products were offered on Walmart.com and
only 30 in a typical physical Walmart store. Leaving aside the best sellers, most products available
online have low sales, but together they account
for a significant portion of Amazon’s total revenue.
This phenomenon, popularly known as the “long
tail” of Internet sales, has been widely documented
(Anderson 2006; Brynjolfsson et al. 2003, 2006).
Interestingly, Amazon itself sells only a small percentage of all products listed on its website; most
1
For expositional ease, we will refer to the seller as “he,” the consumer as “she,” and the platform owner (Amazon) as “it” throughout the paper.
757
Jiang, Jerath, and Srinivasan: Firm Strategies in the “Mid Tail” of Platform-Based Retailing
758
Marketing Science 30(5), pp. 757–775, © 2011 INFORMS
Table 1
Percentage of Products Sold by Amazon in Two Sample Product Categories
Category/subcategory
Total no. of
products
% sold
by Amazon
% sold by Amazon
among top 100 best sellers
Electronics
Accessories & Supplies
Camera & Photo
Car electronics
Computers & Accessories
GPS & Navigation
Home audio & Theater
Marine electronics
Office electronics
Portable audio & Video
Security & Surveillance
Televisions & Video
Tools & Home improvement
Sports & Outdoors
Jewelry
Toys & Games
Shoes
210241750
4071149
4101312
161731
9971543
81453
101433
593
391214
481678
111320
141753
214601108
316951634
112871098
7981977
3441710
700
1005
1001
2303
409
2109
2402
4101
607
1501
1509
604
508
301
302
509
1607
64
62
76
90
73
89
71
83
77
47
66
75
88
76
34
66
72
Source. Data collected from Amazon.com during April 2010.
be tempted to offer them directly, especially if they
show the promise to become best sellers.
A closer examination of product sales on Amazon’s
platform confirms the above intuition—Amazon
indeed sells a disproportionately large number of
high-demand products. For example, although Amazon directly sells only 7% of all electronics products,
it sells 64 of the top 100 best sellers. The third column of Table 1 shows that this is consistently true for
other product categories. Furthermore, the percentage of products sold directly by Amazon decreases
sharply as we go down the list of best sellers. Figure 1
shows an example of this for the “Digital SLR camera” subcategory. In April 2010, this category had 928
products listed; Amazon carried 16 of the top 20 best
sellers but only 5 with sales ranks from 150 to 250.
These statistics further suggest that Amazon seems
to “cherry-pick” relatively high-demand products
from a significant range of mid-tail products for
which the ex ante expected demand is not sufficiently
high for Amazon to readily sell directly but is also
Figure 1
Best Sellers Sold by Amazon in the “Digital SLR Cameras”
Category
8
7
6
5
4
3
2
1
0
1–10
11–20
21–30
31–40
41–50
51–60
61–70
71–80
81–90
91–100
101–110
111–120
121–130
131–140
141–150
151–160
161–170
171–180
181–190
191–200
201–210
211–220
221–230
231–240
241–250
Number of products
sold by Amazon
online retail platforms has become an important phenomenon, especially for long-tail products.
With tens of millions of products available on
Amazon, which ones should it procure and sell
directly, and which ones should it leave to independent sellers to sell? By allowing an independent
seller to sell a product, Amazon captures only a
fraction of the potential profit. However, given the
fixed costs involved in selling a product, selling lowvolume items may not be profitable for Amazon.
On the other hand, for specific niche products, an
entrepreneurial and enterprising independent seller
might face lower fixed costs and may already have
more information than Amazon. (Amazon has data
from the sales of millions of products and can use
these data to identify high-potential products. However, there may still be niche products for which
an independent seller may have better information
on demand compared with Amazon. Anecdotal evidence that we provide subsequently shows that this
is a significant phenomenon.) In this context, Amazon’s proclivity is to directly sell high-volume products and leave the low-volume items to independent
sellers. (The strategy is analogous to that of chain
stores, wherein the firm itself operates the lucrative
city stores but allows franchisees to operate the less
attractive, dispersed suburban and exurban outlets.)
Amazon’s strategy on high-volume best sellers and
low-volume long-tail products is rather obvious—
it will directly sell the high-volume products and
rely on the independent sellers for long-tail products. However, for “mid-tail” products—those that it
cannot classify with certainty as either high-volume
products or low-volume products—Amazon’s strategy is less clear. Although Amazon may let independent sellers offer such mid-tail products, it may also
Sales rank range
Jiang, Jerath, and Srinivasan: Firm Strategies in the “Mid Tail” of Platform-Based Retailing
Marketing Science 30(5), pp. 757–775, © 2011 INFORMS
not sufficiently low to ignore completely.2 Interesting
strategic interactions between Amazon and independent sellers emerge from the uncertainty about the
potential demand of these mid-tail products. For a
mid-tail product whose sales potential is not readily obvious but that can be sold over a significantly long time horizon, Amazon can initially let
the independent seller sell it, track the early sales of
the product, and then decide whether or not to offer
the product directly. And therein lies the inherent risk
faced by a mid-tail independent seller: if the product
sells well, Amazon can observe this (because it processes all sales orders on its website) and will likely
procure and sell the product directly. When Amazon starts selling the product directly, it can boost its
own sales in various ways. For instance, it can prominently display its own offering, and given its advantages in scale and not having to pay its own sales fee,
Amazon typically offers lower prices with very competitive or free shipping. Anecdotal evidence from
popular online blogs and news sources indicates that
Amazon indeed cherry-picks the high-volume products “in store after store and category after category,
where top-selling products once sold by others are
now taken over by Amazon.”3 Once Amazon directly
procures and sells a product, it will essentially “take
all of the sales away from the [independent] seller.”4
This creates a dilemma for the high-demand seller.
He may make more profits early on by selling a high
volume of a product, but if Amazon learns that this
product is worth selling directly, the seller will lose
substantial future sales. Thus, if the seller has a highdemand product, he may have an incentive to reduce
his sales to avoid Amazon’s cherry-picking of his
products. Anecdotal evidence suggests that some sellers strategically reduce their sales by lowering their
services or inventory levels.5 For instance, they may
devote less time and resources to dealing with consumers’ inquiries about their high-demand products
or related postsale services (e.g., they may offer less
customization services such as gift wrapping, or they
may answer product inquiries less conscientiously
and with a longer time lag). These sellers may also
2
We build the intuition here by considering sales rank (which is
based on sales volume) rather than profit. We do this because
Amazon publicly releases sales ranks but not any product-level
profit data. In our formal model, the platform owner makes its
decisions based on profit, which is affected by various factors such
as demand levels, the marginal cost of procurement, and the price
sensitivity for the product.
3
See Mikailizadeh (2010).
4
See McFarland (2009).
5
See McFarland (2010).
759
carry a lower inventory level and periodically create stockout situations.6 Such service interactions with
the consumer typically occur outside Amazon’s retail
platform and cannot be directly observed by Amazon.
Moreover, with hundreds of thousands of independent sellers, Amazon may find it too costly to monitor
even the somewhat observable aspects of seller services. Hence, Amazon may face a demand-learning
problem for mid-tail products—if it observes not-sohigh unit sales for the seller’s product, it may not
be able to infer whether or not the product has the
potential for high enough sales to warrant direct selling, because the observed not-so-high sales may be a
result of either a not-so-popular product or a popular
product but not-so-good seller services/efforts.
To prevent this to some extent, Amazon requires a
baseline level of services from the sellers, and it also
expends resources to acquire consumer reviews in an
attempt to prevent poor services that can damage the
reputation of its platform. Many anecdotes indicate
that Amazon immediately terminates any sellers who
are identified as giving poor services. For this reason,
sellers always want to provide “acceptable” levels of
service to meet Amazon’s standard or normal service
levels. However, sellers still have a lot of leeway in
deciding on how much additional (or “exceptional”)
service to provide beyond the standard service level.
For example, gift wrapping or other customizable service options, the promise of faster shipment, high
stock availability, and exceptional product support are
all beyond the standard service requirements. These
factors cannot be costlessly monitored by Amazon but
certainly affect the seller’s sales, enabling the seller to
mask his high demand from Amazon. Furthermore,
the seller’s promotions or other selling efforts that
influence the demand but are not directly observed by
Amazon are also included in the unobserved services
that make demand masking possible.
6
We conducted a small empirical exercise to check for evidence of
sellers manipulating their service levels. We selected eight thirdparty sellers on Amazon selling mid-tail products (with sales ranks
in the upper middle range). We picked different digital cameras
and rice cookers, none of which were directly sold by Amazon
at that time. Using two different customer e-mail accounts, we emailed two inquiries to each seller about two of their products. Two
types of questions were in each e-mail: some product-specific (e.g.,
whether a camera’s frame is metal or plastic) and some servicespecific (e.g., whether they offer gift wrapping or can help write
a gift note or send packages without enclosing price information,
etc.). We found a large variation in response time (varying from two
hours to over five days) across products for the same seller (six out
of eight sellers provided very different service levels for the two
product inquiries). Although the above exercise is not conclusive,
and the different amounts of delay could be due to some random
factors, the fact that the same seller takes significantly different
amounts of time to respond to similar questions about different
products indicates that sellers could indeed be varying their service
levels strategically.
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Jiang, Jerath, and Srinivasan: Firm Strategies in the “Mid Tail” of Platform-Based Retailing
Whereas this above discussion is in the context of
Amazon, the key forces at play are relevant to online
platform retailing in general. Therefore, mid-tail products give rise to an interesting market in which the
independent seller benefits from selling on the platform, but he may also be in competition with the
platform owner itself. The platform owner can track
the seller’s sales to identify whether his product has
high enough demand for it to sell directly. Sales,
however, are the outcome of the inherent “popularity level” of the product (because of its design and
other attributes) and the seller’s demand-enhancing
services, both of which are unobservable to the platform owner. Under the threat of entry by the platform owner, high-demand sellers may attempt to
mask themselves as low-demand sellers by providing
“acceptable,” but not “exceptional,” service so that
they can continue selling in the future.
This motivates interesting research questions: What
implications do such conflicting interests have for the
platform owner, the high-demand seller, and the lowdemand seller? What fee should the platform owner
charge? How will different sellers respond in terms
of their service provisions? Under what conditions
will the platform owner be able to separate the highdemand mid-tail products from the low-demand midtail or long-tail products? Is it ever optimal for the
platform owner to forgo its option to sell the product directly? How are consumers affected? Finally, if
the platform owner can acquire fully revealing seller
reviews, how does this affect the answers to the above
questions?
We study these strategic interactions and provide
novel insights into the dynamics of the mid tail of
online retailing. First, we find that if the platform
owner believes ex ante expected demand to be sufficiently high, it will set its fee high enough to separate
the high-demand seller from the low-demand seller.
In this case, only the high-demand seller will sell on
the platform in the early period (separating equilibrium), and the platform owner will subsequently sell
the high-demand product directly. In the case of a
low ex ante probability of high demand, however, the
platform owner will set its per-unit fee low enough
so that even a low-demand seller will participate on
the platform. However, this enables the high-demand
seller to mimic a low-demand seller by underinvesting in demand-enhancing services so that the platform owner will be unable to learn the seller’s true
demand (pooling equilibrium).
Second, the platform owner may be better off to
contractually forgo its option to sell the independent
seller’s product. This is because, without the threat of
entry by the platform owner, the high-demand seller
will optimally provide a high level of service and
have high sales from which the platform owner can
Marketing Science 30(5), pp. 757–775, © 2011 INFORMS
benefit by charging higher fees. One may expect that
sellers prefer less threat of entry. Interestingly, however, we find that both the low-demand and the highdemand sellers may benefit from the platform owner‘s
threat of entry. This is primarily because if the ex ante
probability of high demand is small, the platform
owner’s entry option will lead to a lower per-unit fee
than without the threat of entry.
Third, the platform owner’s entry option can
reduce consumer surplus early in the product selling
horizon, although it increases consumer surplus late
in the selling horizon. Finally, if the platform owner
invests in consumer reviews that fully reveal a seller’s
service level (and, therefore, his true type), then its
optimal sales fee will increase (from the no-review
case) if the ex ante probability of a high-demand type
is low and decrease if that probability is high.
The rest of this paper is organized as follows. In
the next section, we briefly review the related literature. In §3, we develop an analytical framework to
model the interaction between the platform owner
and the independent seller. In §4, we first examine
the complete information case; then, we analyze the
incomplete information case and compare two scenarios: (1) the platform owner credibly commits to not
selling the product, and (2) it retains the option to sell
the product in the future. In §5, we examine the effect
of consumer reviews. In §6, we discuss the robustness
of our insights to alternative modeling assumptions.
In §7, we conclude the paper with a short discussion.
2.
Review of Relevant Literature
Our work lies at the intersection of Internet retailing,
platform-based business models, stores within a store,
asymmetric information strategies (especially signaling), and signaling under moral hazard. Although one
and occasionally more than one aspect has been studied at a time, the rich interaction examined here is
unique and without much precedent. To clearly delineate our contributions, we briefly discuss the relevant
aspects of each literature stream.
Prior work on Internet retailing has primarily
focused on the interaction between online and
off-line consumer purchasing (Ansari et al. 2008,
Biyalogorsky and Naik 2003, Choi et al. 2010, Choi
and Bell 2011, Neslin et al. 2006, Ofek et al. 2009,
Pan et al. 2002b, Shankar et al. 2003), the impact of
easier online information searches on prices (Bakos
1997, Baye et al. 2007, Brynjolfsson and Smith 2000,
Pan et al. 2002a), empirically documenting the “longtail” phenomenon and its implications (Brynjofsson
et al. 2003, 2006; Elberse 2008; Tan and Netessine 2009;
Tucker and Zhang 2011), and studying the effects of
reviews on firm marketing strategies (e.g., Chen and
Jiang, Jerath, and Srinivasan: Firm Strategies in the “Mid Tail” of Platform-Based Retailing
Marketing Science 30(5), pp. 757–775, © 2011 INFORMS
Xie 2005, Jiang and Srinivasan 2011, Kuksov and Xie
2010). However, as far as we know, our research is
the first to identify and analytically study strategic
interactions of the aforementioned nature in platformbased Internet retailing.
With the advent of new technologies, platformbased business models are becoming increasingly
popular. Beyond Amazon’s retail platform, there is
a plethora of products and services being turned
into a platform on which sellers and end users can
directly interact and through which a wide range
of products can be offered. Prominent examples
include eBay for auctions; iPhone, Android OS, and
iPad for software applications; and Microsoft Xbox,
Sony PlayStation, and Nintendo Wii for console-based
video games. These developments have motivated the
recent literature on two-sided markets (Armstrong
2006, Eisenmann et al. 2006, Parker and Van Alstyne
2005, Rochet and Tirole 2003). This literature primarily focuses on cross-market network effects. In
contrast, our focus is not on the platform owner’s
optimal marketing mix to develop or benefit from
its two-sided network. The core of our analysis
arises from the aforementioned opposing incentives—
strategic learning of demand by the platform owner
versus strategic masking of demand by the highdemand seller.
Our work is related to the vast literature on
distribution channels in marketing (Coughlan and
Wernerfelt 1989, Desai et al. 2004, Desiraju and
Moorthy 1997, Iyer and Villas-Boas 2003, Jeuland
and Shugan 1983, McGuire and Staelin 1983,
Moorthy 1988). Specifically, “stores within a store”
(e.g., cosmetics boutiques run by manufacturers in
large department stores) can also be considered as
platform-based retailing in physical stores. Jerath and
Zhang (2010) show that channel efficiency and price
competition considerations are the drivers behind
the choice of this arrangement. Online platformbased retailing, however, generates a completely different set of issues. First, the number of products
sold on online platforms is several orders of magnitude larger than that sold at any physical retailer—
which, because of its shelf-space limitation, typically
sells only mainstream products—leading to a complex demand identification problem in our current
study. Second, because of large investments and strict
long-term contracts involved, opportunistic behavior
on the part of the parent store is limited in a physical store-within-a-store arrangement. However, in the
online setting, the platform owner’s cherry-picking of
third-party sellers’ successful products is easily facilitated because of the low investment and the shortterm “at-will” nature of their agreement.
Besides contributing to the existing literature on
retailing, we also obtain some interesting results for
761
asymmetric information games. First, in most signaling games, a separating equilibrium in which a
high-type player separates from a low-type player
is the focal equilibrium (e.g., Desai 2000, Desai and
Srinivasan 1995, Moorthy and Srinivasan 1995, Shin
2005, Simester 1995, Soberman 2003). In contrast, in
our scenario, a high-demand seller wants to imitate
a low-demand seller to avoid the platform owner’s
entry, whereas a low-demand seller is unconcerned
and plays his optimal strategy—the pooling outcome
is the focal equilibrium. This is related to the literature on countersignaling (Araujo et al. 2008, Feltovich
et al. 2002, Mayzlin and Shin 2011, Teoh and Hwang
1991), but the intent of the high-type player in our
case is to hide, rather than reveal, his true type.
Second, most research on signaling does not consider unobservable actions and examines only the signaling of private information from the principal to
the agent. In contrast, our research concerns both
signaling of private information and unobservable
actions This is similar to Desai and Srinivasan (1995),
who study how a franchisor may signal its product’s
high-demand potential to an uninformed franchisee,
whose unobservable effort also influences demand.
Our model differs structurally in that both the private
information about demand and the unobserved effort
(service level) are possessed by the same party (the
seller) rather than by different parties. More importantly, in our setting, the uninformed party (the platform owner) has to first decide its fee before observing
the seller’s signal about product demand and subsequently decides whether or not to procure and sell
the product directly.
3.
Model
Consider a new product available for sale on an
online retail platform such as Amazon.com. For the
ease of understanding and exposition, we will refer
to the platform owner as Amazon, although our analysis applies to other such retail platforms. Amazon
can sell the product directly, or it can let an independent seller offer it and charge him a per-unit fee
for each sale. A fixed cost is incurred to sell the
new product. Such a fixed cost may include establishing relationships and negotiating contracts with
the manufacturers, arranging logistics, and allocating warehouse spaces. An independent seller may
have a significantly lower fixed cost (for the product under consideration) than Amazon. In fact, the
seller’s fixed cost may be sunk. For example, the
seller may leverage his existing personal connections
to procure the product from its manufacturers, and
he may use his home basement to store and manage
inventory. In addition, the seller may sell only a few
products and thus may not have any costly logistical
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Jiang, Jerath, and Srinivasan: Firm Strategies in the “Mid Tail” of Platform-Based Retailing
issues that Amazon faces because it carries hundreds
of thousands of products. Collectively, these factors
may enable some independent sellers to enjoy a fixed
cost substantially lower than that of Amazon. Without loss of generality, we assume that the independent
seller has zero or sunk fixed cost, whereas Amazon
must incur a positive fixed cost (F > 0) to sell the new
product.
We consider a dynamic model with two time periods. The product can be sold in both time periods,
and demand in each period i (denoted by a parenthesized superscript i ∈ 811 295 is represented by a linear
function: q 4i5 4p1 e5 = ƒ + e4i5 − bp4i5 , where p is the price
of the product, e is the service (or selling effort) level
by the party selling the product (either Amazon or the
independent seller), and ƒ and b are constants.7 There
is uncertainty about the overall product demand—
with a prior probability ˆ > 0, ƒ = ƒH , and with a
probability 1 − ˆ, ƒ = ƒ L < ƒH . For ease of exposition,
we reframe the uncertainty in the product demand
as uncertainty about the seller’s type, which is H
with probability ˆ and L with probability 1 − ˆ. The
seller knows his type (i.e., whether his product has
low or high demand), whereas Amazon knows only
the prior probability distribution. This assumption
that ex ante the seller knows more about the product
demand than Amazon is quite reasonable. For example, a local retailer knows which of his products are
selling well locally and may decide to sell them online
to a larger customer base. An international immigrant
may know about a product that sells well in his own
country and can order the product from the manufacturer there to sell on Amazon. In general, it is very
plausible that a small seller may have better market
demand information than Amazon for the particular
product he has identified to sell. Although Amazon
may have better knowledge about the demand for
many mainstream products, it is reasonable to assume
that Amazon does not always have ex ante better
demand information than all third-party sellers for
millions of long-tail and niche products. In fact, our
interest is in those products whose levels of demand
are not already known to Amazon.
We assume that the selling party’s service level
influences the total demand. A service level e imposes
a per-unit marginal cost of s4e5 = ke2 on the selling
party, where k is a constant and e ≥ 0. For a more
interesting analysis, we assume that the parameters
are such that the following conditions hold.
7
We assume for analytical tractability that the overall demand
intercept is separable in ƒ and e. However, our insights will hold
for other functions that allow ƒ and e to jointly influence the
y
demand intercept (e.g., a multiplicative form ƒ x 4e4i5 5 , x > 0, y > 0,
will provide the same insights).
Marketing Science 30(5), pp. 757–775, © 2011 INFORMS
Condition C1. (i)
F >
ˆ4ƒH + 1/44bk5 − bc52 + 41 − ˆ54ƒL + 1/44bk5 − bc52
4b
−
6ˆ4ƒH − ƒL 5 + ƒL + 1/44bk5 − bc72
3
8b
(ii) F < 4ƒH + 1/44bk5 − bc52 /48b5.
Condition C2. ƒL < ƒH ≤ ƒL + 1/42bk50
C1(i) ensures that the fixed cost is high enough,
such that with only the prior information on the
seller’s type, Amazon will make a higher expected
profit by allowing the seller to sell the product than
by selling it directly. C1(ii) ensures that the fixed cost
F is not too high, such that if Amazon knows that
ƒ = ƒH (i.e., the demand is high), it prefers selling the
product directly rather than letting the independent
seller do so. Consequently, when assumption C1 is
satisfied, Amazon will allow the independent seller
to sell the product if it does not know the true value
of ƒ, but Amazon will sell the product directly if it
knows ƒ = ƒH .
Amazon gains on two grounds by letting the seller
offer the product on its platform. First, it earns a fee
for each unit sold by the seller. Second, Amazon can
acquire more information on market demand because
it has direct access to the seller’s sales information
(price and quantity sold). If the seller’s sales are high
(i.e., an H-type seller), Amazon will procure and sell
the product directly. When Amazon itself sells a product, it can set a lower price than the independent
seller because it does not have to pay its own fees
(hence avoiding the “double-marginalization” problem). In addition, Amazon can negotiate better prices
from the manufacturer, prominently promote its own
products to consumers, and offer cheaper/free shipping. Therefore, consumers are much more likely to
buy the product from Amazon than from any independent seller if both offer it. As discussed in §1, the
independent seller’s sales will plummet to essentially
zero once Amazon directly sells his product. Thus, we
make a reasonable simplification that the independent
seller will make zero profit (i.e., Amazon effectively
replaces the seller) once Amazon starts directly selling
his product.8
Under Amazon’s entry threat, the H-type seller has
an incentive to hide his high demand by reducing
his services. As discussed earlier, many aspects of
service are such that they are transacted outside the
platform and are not directly observed by Amazon.
Because Amazon observes both the price and quantity sold, in essence, the seller’s price–quantity pair
8
Our results are robust and qualitatively the same as long as the
seller’s profit is significantly lower when Amazon sells his product
than when Amazon does not sell that product.
Jiang, Jerath, and Srinivasan: Firm Strategies in the “Mid Tail” of Platform-Based Retailing
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Marketing Science 30(5), pp. 757–775, © 2011 INFORMS
acts as the seller’s signal of his type. The seller can
use his unobservable service level to manipulate the
signal. Assumption C2 ensures that the H-type seller
can use services to create an uninformative signal to
prevent Amazon from learning his type. Intuitively,
the H-type seller can set his service level and price
such that if Amazon observes not-very-high sales, it
cannot determine whether this is because ƒ = ƒL and
the service provided is optimal, or because ƒ = ƒH but
the service is below the optimal level.
Our model encompasses both asymmetric information (Amazon does not know the seller’s type) and
moral hazard (Amazon also does not observe the
seller’s service provision). Previous research in the
contracting literature has shown that a menu of contracts can be used by a principal to separate different
types of agents under asymmetric information (Lal
and Staelin 1986, Rao 1990). Furthermore, a two-part
tariff can be used with risk-neutral agents to avoid the
moral hazard problem (Holmstrom 1979). We adopt a
pure variable fee structure in our model based on the
actual contract form adopted by Amazon.9 With millions of products and hundreds of thousands of independent sellers on the platform, a menu of contracts
or nonlinear contracts where each contract has multiple components may be very difficult to design or
implement. The simplicity of implementing one variable fee structure across all sellers may be the reason
why it is adopted by Amazon and many other platforms such as iPhone App Store and Google Android
Market. Note, however, that using a nonlinear contract will not qualitatively change our main results.
The two-period game proceeds as follows. In the
first period, “nature” determines the seller’s type.
With probability ˆ the seller is an H-type, and
with probability 1 − ˆ the seller is an L-type. The
seller learns his type with certainty, whereas Amazon
knows only the probability distribution. Amazon first
selects a per-unit fee f to charge to the seller. We fix
Amazon’s fee to be the same across the two periods
because, with millions of products sold by independent sellers, a renegotiation or dynamic change of this
fee is likely to be costly and is not observed in reality.
Given f , the seller chooses whether or not to sell
on Amazon; if he decides to sell, he simultaneously
415
chooses his first-period service level 4et 5 and price
415
4pt 5, t ∈ 8L1 H 9. Then, the seller’s sales are realized
415
415
415
415
according to the demand q 415 4pt 1 et 5 = ƒt +et −bpt ,
9
In addition to its per-unit fee, Amazon does charge the sellers a
small fee of $39 per month, which gives the sellers access to certain
services such as adding new products or updating product/seller
information displayed. However, because even small professional
sellers have monthly sales much higher than many thousands of
dollars, this small monthly fee is, in all probability, not levied with
the intent of removing moral hazard.
Table 2
Key Notations
Variables/
Symbols
t
ˆ
i
f
Description
The independent seller’s type; t = “H” or “L.”
The probability (ex ante) that the seller’s type is “H.”
Time period; i = 1 or 2.
The fee Amazon charges the seller for each unit sold.
4i5
Type t seller’s service level in period i.
Marginal cost of offering service level e2 s4e5 = ke2 ,
where k > 0 is constant.
Type t seller’s price in period i.
et
s
4i5
pt
4i5
4i5
4i5
4i5
Type t seller’s demand in period i: qt = ƒt + et − bpt ,
where b is constant.
ƒt
Type t seller’s demand intercept excluding the effect of
his service: ƒH > ƒL .
â
The overall demand intercept observed by Amazon:
415
415
415
â ≡ ƒt + et = qt + bpt .
c
The marginal cost of the product.
F
Fixed cost required for Amazon itself to sell a product
directly.
415
415
Œ4H — pt 1 qt 5 Amazon’s posterior belief that the seller is of type H after
415
415
observing pt and qt .
4i5
çA
Amazon’s expected profit in period i.
qt
çA
4i5
çt
çt
ˆ
¯
sep, pool
rev
Amazon’s overall expected profit for both periods i = 1
or 2.
Type t seller’s profit in period i.
Type t seller’s overall profit for both periods i = 1 or 2.
The hat over a variable indicates the case of complete
information.
The bar over a variable indicates the case of no entry
threat by Amazon.
These subscripts indicate the separating and pooling
outcomes, respectively.
This subscript indicates that the variable is for the case
with seller reviews.
and both the seller and Amazon realize their respective profits.
At the beginning of the second period, Amazon will
update its belief about the seller’s type after observing
the seller’s first-period price and sales. Based on the
updated belief, Amazon will decide whether or not
to sell the product directly. If Amazon sells the product directly, it will simultaneously choose its service
level (eA 5 and price (pA 5. If Amazon decides not to
enter the market, the seller will then simultaneously
425
choose his second-period service level 4et 5 and price
425
4pt 5. Demand is then realized based on the secondperiod price and service levels. All key notations are
summarized in Table 2.
4.
Analysis
We organize our analysis in the following way. In §4.1,
we analyze a benchmark case of complete information, in which Amazon knows the true demand (i.e.,
the seller’s type). In §4.2, we analyze another benchmark case of asymmetric information and unobserv-
Jiang, Jerath, and Srinivasan: Firm Strategies in the “Mid Tail” of Platform-Based Retailing
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able service, in which Amazon contractually commits
to not selling the product. In §4.3, we examine our
focal case of asymmetric information and unobservable service in which Amazon retains the option to
sell the product.
4.1. Complete Information
In this section, we examine a complete-information
game in which Amazon knows the seller’s type. Without information asymmetry, the game becomes simple to solve. If the demand is low (ƒ = ƒL 5, Amazon
will let the independent seller sell the product in both
periods. Given Amazon’s fee fˆ, the L-type seller will
select the same service levels and prices for both periods i ∈ 811 29. (We will use a “hat” over the variable to
indicate the case of complete information.) The L-type
seller’s total profit from both periods is given by
2 X
4i5
4i5 4i5
4i5 ç̂L =
4ƒL + êL − b p̂L 5 p̂L − c − fˆ − k4êL 52 1
i=1
where c > 0 is the product’s marginal cost.10 Solving the first-order conditions, one easily finds the Ltype seller’s optimal (first-best) service level and price:
∗4i5
∗4i5
êL = 1/42bk5 and p̂L = 4ƒL + b4c + fˆ5 + 3/44bk55/42b5,
respectively. The corresponding profit is given by
ç̂∗L 4fˆ5 =
4ƒL − b4c + fˆ55 + 1/44bk52
0
2b
Amazon’s profit in the case of an L-type seller is
P
4i5
4i5
given by ç̂A1 L 4fˆ5 = 2i=1 8fˆq̂L 4fˆ59, where q̂L 4fˆ5 =
∗4i5
∗4i5
ƒL + êL − b p̂L 4fˆ5 is the seller’s quantity sold in
period i as a function of fˆ. Thus, Amazon’s optimal
fee is fˆ∗ = 4ƒ − bc + 1/44bk55/42b5, and its profit from
L
the L-type seller is ç̂∗A1 L = 4ƒL − bc + 1/44bk552 /44b5.
If the demand is high (ƒ = ƒH 5, Amazon will sell
the product directly in both periods. In this case, its
optimal service level and price are easily found to
∗4i5
∗4i5
be eA = 1/42bk5 and pA = 4ƒH + bc + 3/44bk55/42b5,
respectively, with a corresponding total profit of
ç̂∗A1 H = 264ƒH − bc + 1/44bk552 /44b5 − F 7.
4.2.
The Platform Owner Commits to “No Entry”
in the Second Period
In this section, we analyze the case of asymmetric information and unobservable service in which
Amazon contractually commits to not selling the
product in the future.11 This removes the H-type
seller’s incentive to mask his demand. Therefore, with
Amazon’s credible commitment to “no entry,” the
seller, irrespective of his type, will choose his “firstbest” service level and price according to his type,
given Amazon’s per-unit fee. We will later analyze
whether or not it is advantageous for Amazon to
forgo its option of entry.
The seller will select the same service levels and
prices for both periods i ∈ 811 29. His total profit
P
4i5
from both periods is given by ç̄t = 2i=1 84ƒt + ēt −
4i5
4i5
4i5
b p̄t 56p̄t − c − f¯ − k4ēt 52 79, where t ∈ 8L1 H 9 represents
the seller’s type. Given Amazon’s per-unit fee f¯, the
4i5
4i5
seller chooses the service levels (ēt 5 and prices (p̄t 5
to maximize his total profit. (Throughout this paper,
we use a “bar” over any variable to indicate that the
variable is for the case of no entry threat by Amazon.)
Lemma 1. Without threat of entry by the platform
owner, both types of sellers will offer the same optimal service levels in both periods; their prices and profits differ
(separate) according to their types.
Lemma 1 shows that if Amazon commits to not
entering the market, both types of sellers will, in equilibrium, offer the same (high) service level. The prices
and profits, however, differ across the two types.12
The equilibrium outcome (service levels, prices, fees,
and overall profits for a seller of type t and for
Amazon) are provided in the appendix.
4.3.
The Platform Owner Retains Its
Entry Option
In this section, we study our focal case in which
Amazon keeps its option to sell the product directly
in the second period and will do so if it identifies
the seller as an H-type seller. Under different parameter conditions, we obtain either a separating equilibrium (in which Amazon can determine the seller’s
type after the first period) or a pooling equilibrium
(in which it cannot).
4.3.1. The Platform Owner Learns the Independent Seller’s Type: Separating Equilibrium. In this
equilibrium, Amazon is able to learn the seller’s true
type after the first period. Amazon will directly sell
the product in the second period only if it identifies the seller as an H-type. Note that it is not possible to have a separating equilibrium with any fee
f < 4ƒL − bc + 1/44bk55/b. This is because at such a
fee, both types of sellers sell on the platform, and
11
10
For analytical simplicity and without loss of generality, we
assume the discount rate to be 1 across the two periods. Our main
results stay qualitatively the same if we allow for discounting
of the second-period profit; only the parameter regions of those
results will change depending on the discount rate.
Amazon can make a legally binding credible commitment of
this nature by putting in its seller agreement verbiage such as
“Amazon.com Inc. cannot contract with a product’s original manufacturer to directly sell the product in competition with the thirdparty seller without specific permission from the seller.”
12
All proofs in this paper are relegated to the appendix.
Jiang, Jerath, and Srinivasan: Firm Strategies in the “Mid Tail” of Platform-Based Retailing
Marketing Science 30(5), pp. 757–775, © 2011 INFORMS
the H-type strictly prefers to mimic the L-type to
avoid Amazon’s entry. (Given f , the H-type’s separating equilibrium profit is weakly less than what
he can earn in two periods if he mimics the L-type
in the first period to deter Amazon’s entry.) In contrast, any fee f satisfying 4ƒL − bc + 1/44bk55/b ≤ f <
4ƒH − bc + 1/44bk55/b will induce a separating equilibrium because with such a fee, only the H -type seller
will profitably sell a positive quantity (the L-type will
not enter the market).13 Thus, the H-type seller does
not have any incentive to mimic the L-type and will
choose his first-best service level and price (conditional on f 5. In other words, the H-type seller makes
a positive profit in the first period and zero profit
in the second period during which Amazon will sell
the product directly.14 Therefore, with probability ˆ,
Amazon earns some fees from the H -type seller in the
first period and will sell the product itself in the second period. If the seller is an L-type, which happens
with probability 1 − ˆ, Amazon will earn zero profit.
We use the subscript “sep” to indicate the separat∗
ing outcome. In the appendix, we compute fsep
, ç∗t1 sep ,
∗
and çA1 sep . In §4.3.3, we specify in Proposition 1 the
condition under which this separating equilibrium is
realized.
4.3.2. The Platform Owner Does Not Learn the
Independent Seller’s Type: Pooling Equilibrium.
We now consider the case of f < 4ƒL − bc + 1/44bk55/b,
in which both types of sellers will sell on Amazon’s
platform. Note that if the realized equilibrium corresponds to f < 4ƒL − bc + 1/44bk55/b, then a pooling equilibrium arises because given such a fee, the
H-type seller strictly prefers to mimic the L-type
to avoid Amazon’s entry in the second period.
Because the seller knows his own type with certainty, for sequential equilibrium, we need to specify only Amazon’s posterior belief about the seller’s
type. There can be infinitely many pooling equilibria supported by different out-of-equilibrium beliefs.
However, in our case, all such equilibria except one
are ruled out or refined away by specifying what
beliefs are “unreasonable” using the “intuitive criterion” by Cho and Kreps (1987) and additional logical reasoning. In the electronic companion (available
13
The upper bound is needed because with f ≥ 4ƒH − bc + 1/
44bk55/b, neither type of seller can profitably sell on Amazon.
14
According to his demand function qL = ƒL + eL − bpL , to sell
any positive quantity, the L-type seller must charge a price pL <
4ƒL + eL 5/b. If f ≥ 4ƒL − bc + 1/44bk55/b, the L-type’s profit margin
becomes
ƒ − bc + 1/44bk5
ƒ + eL
−c− L
− keL2
pL − c − f − keL2 < L
b
b
2
e − bkeL2 + 1/44bk5
1
= L
= −k eL −
< 00
b
2bk
Hence, he will not sell on Amazon if its fee is so high.
765
as part of the online version that can be found at
http://mktsci.pubs.informs.org/), we show that such
refinements lead to the following unique pooling
equilibrium: in the first period, both types of sell∗415
ers choose pt 4f 5 = 4ƒL + b4c + f 5 + 3/44bk55/42b5 and
∗415
sell a quantity of qt 4f 5 = 4ƒL − b4c + f 5 + 1/44bk55/2.
This outcome corresponds to the L-type seller choosing his first-best service level and price, given f .
Below is Amazon’s posterior belief that supports
this unique pooling equilibrium. For convenience, we
415
define the overall demand intercept as â ≡ qt +
415
415
bpt = ƒt + et :

1


1
11 if â > ƒL +


2bk



415
415
Œ4H — pt 1 qt 5 = ˆ1 if ƒ ≤ â ≤ ƒ + 1 1 (1)

H
L

2bk





01 if â < ƒH
Again, we remind the reader that Proposition 1 will
specify the condition for this pooling equilibrium outcome to occur. We now derive this equilibrium.
In the second (and last) period, the seller faces
no future entry threat and will thus choose his firstbest service level and price, conditional on Amazon’s fee f . Hence, in the second period, a seller
∗425
∗425
of type t will choose et = 1/42bk5 and pt 4f 5 =
4ƒt + b4c + f 5 + 3/44bk55/42b5, which are the same
as (3) and (5) in the appendix, respectively. The
∗425
seller’s second-period profit is given by çt 4f 5 =
2
644ƒt − b4c + f 5 + 1/44bk557 /44b5.
415
Amazon observes the seller’s first-period price pt
415
and unit sales qt because it processes all orders
415
415
on its platform. In effect, pt and qt are a multidimensional signal of the seller’s type. After the first
415
415
period, having observed pt and qt , Amazon learns
415
415
415
the overall demand intercept â =ƒt + et = qt + bpt ,
but it may not be able to deduce ƒt or the seller’s type
415
because it does not observe et .
Note that an L-type seller has no incentive to prevent Amazon from learning his true type because
Amazon, knowing that he is an L-type, will not enter
the market. Note also that at any given f that is
not too high to preclude the L-type seller from selling profitably, the L-type seller is actually indifferent between the pooling and separating outcomes
because both outcomes lead to no entry by Amazon.
This implies that an L-type seller will play his firstbest strategy as long as Amazon’s belief will not
falsely identify him as an H -type for doing so, which
is the case for the belief system (1). In contrast, an
H-type seller facing the threat of entry by Amazon
has an incentive to strategically choose his first-period
service level and price to exactly mimic the L-type
seller’s first-best price and sales. Such a strategy by
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the H -type seller results in a unique pooling outcome
and prevents Amazon from learning his true type.
Therefore, Amazon will not enter the market in the
second period.
We now analyze the implications of this pooling
equilibrium in detail. At this equilibrium, Amazon is
unable to determine the seller’s type after the first
period and hence will not directly sell the product
in the second period. Because the second period is
the final period, the seller will face no future entry
threat by Amazon and hence will set the service level
and price to maximize his profit according to his true
demand. Thus, given f , the seller’s optimal service
level and price in the second period are the same as
those in §4.2. We use the subscript “pool” to indicate that a variable corresponds to the pooling outcome. The possible pooling equilibrium outcome is
provided in the appendix.
4.3.3. Realized Equilibrium. Proposition 1 shows
that when the probability of H-type is below a threshold, the pooling equilibrium is realized; otherwise, the
separating equilibrium is realized.
Proposition 1. For any set of values of the other
parameters, there exists ˆ ∗ ∈ 401 15 such that the pooling
equilibrium outcome is realized if ˆ < ˆ ∗ and the separating
equilibrium outcome is realized if ˆ ≥ ˆ ∗ .
Figure 2 illustrates the equilibrium realizations
in the (ƒH 1 ˆ) parameter space. In the figure, the
curve AC corresponds to the boundary defined by
assumption C1(i), the line AB corresponds to the
boundary defined by assumption C1(ii), the line CD
corresponds to the right-side boundary of assumption C2, and the curve EC corresponds to ˆ ∗ . If the
ex ante expected demand is high enough (i.e., ˆ and
ƒH are in the “Short tail” region), Amazon will have
entered the market in the first period. Products such
as a new version of a highly popular digital camera
are likely to have parameters that fall into this region;
Market Outcomes in 4ƒH 1 ˆ5 Parameter Space
Figure 2
A
Prior probability of high demand
1.0
Hig
h fe
S e
ep
(pla arati
tfor ng
mo
wn
er
E
Long tail
(no entry
by platform
owner)
0.0
1.0
L = 1
Short tail
(ex ante entry by platform owner)
lea
rns
dem
and
)
Low fee Pooling
(platform owner can learn demand
but chooses not to)
B
High-demand intercept H
C
D
2.0
there is still demand uncertainty for such products,
but their expected demand is high enough to warrant
Amazon’s direct selling immediately. The left rectangular “Long tail” region represents the very lowdemand, long-tail products for which even ƒ H is small
enough such that Amazon will not be able recover
its fixed cost if it sells them directly. Our analysis has
focused on the most strategically interesting parameter region—the mid-tail region where the expected
demand is in the middle range. We find two qualitatively different mid-tail regions. In the “Separating”
parameter region, the expected demand is relatively
high, and at equilibrium, Amazon will set its fee high
enough to separate both types of sellers to directly sell
the high-demand product in the second period. In the
“Pooling” region, the expected demand is relatively
low, and Amazon actually finds it optimal not to learn
the seller’s true type and will set a fee low enough to
allow both types of sellers to enter the market. In that
case, in the first period, the H-type seller will mimic
the L-type by strategically lowering his service level,
and in the second period, Amazon will not enter the
market because it cannot learn the seller’s type. In
contrast to the extant literature on signaling, which
has focused on separating equilibrium outcomes, the
focal outcome in our paper is the pooling equilibrium.
Now, we examine how Amazon’s entry option
affects its own profit.
Proposition 2. If ˆ < ˆ ∗ , the platform owner’s fee and
its expected profit are both lower if it retains its entry
option than if it forgoes it.
Proposition 2 shows that in the pooling parameter region, Amazon’s entry option will hurt its own
profit. Amazon is worse off in the pooling equilibrium
than if it forgoes its future option to sell the product directly. This is because Amazon’s threat of entry
gives the H-type seller an incentive to reduce his firstperiod service level to mimic the L-type seller so that
Amazon is unable to learn his type and hence will
not enter the market in the second period. If Amazon
ex ante forgoes its entry option, the H-type seller will
then optimally provide a high service level even in
the first period, and in turn, Amazon will have an
incentive to charge a higher fee to benefit from the
H-type seller’s high sales. As a result, in the pooling
parameter region, Amazon’s fee is lower if it retains
an entry option than if it forgoes it. Amazon’s overall
profit is also lower when it retains the entry option
because of both its lower per-unit fee and the H-type
seller’s strategically reduced first-period sales.
One managerial implication is that if Amazon can
do so costlessly, it should commit to no entry for
products with parameters that fall in the pooling
region. In addition, our analysis shows that Amazon’s
optimal fee may differ across products depending on
Jiang, Jerath, and Srinivasan: Firm Strategies in the “Mid Tail” of Platform-Based Retailing
Marketing Science 30(5), pp. 757–775, © 2011 INFORMS
the parameters associated with the products. However, in practice, with tens of millions of products on
its platform, Amazon cannot very cost-efficiently contract on a product-by-product level; in fact, its fees
vary only across product categories, e.g., 6% for computers, 8% for cameras, 10% for tires and wheels, 12%
for musical instruments, and 15% for toys and video
games. Given that in practice Amazon uses only one
blanket seller contract, if it commits to no entry, it
solves the moral hazard problem, but it will give up
the profit potential from cherry-picking of the thirdparty sellers’ high-demand products. According to
Amazon’s annual reports, Amazon makes most of its
profits from direct selling. Even though it directly sells
only about 7% of the products listed on its platform,
its sales account for 69% of all unit sales on its platform. Thus, it is understandable that if Amazon uses
a blanket contract for all third-party sellers, it does
not want to forgo its entry option.
Now we examine how Amazon’s entry option
affects the third-party seller and the consumers. Intuitively, one may expect that a seller prefers less threat
of entry and that consumers will benefit from potential competition in the market. However, we find that
this is not necessarily the case.
Proposition 3. If ˆ < ˆ ∗ , the L-type seller makes a
higher profit with the platform owner’s threat of entry than
without it. The H -type seller makes a higher profit with
the platform owner’s threat of entry than without it only
if ƒH < ƒ ∗ . (Both ˆ ∗ and ƒ ∗ are constant expressions given
in the appendix.)
According to Proposition 3, in the pooling parameter region, the L-type seller will benefit from
Amazon’s threat of entry. The intuition is that with or
without Amazon’s entry threat, the L-type seller will
choose the same service level and will set his firstbest price given Amazon’s fee, but Amazon’s fee is
lower when it retains its entry option. Of course, if
the separating outcome is realized as in the case of
ˆ > ˆ ∗ , the L-type seller is hurt by Amazon’s entry
option because he sells nothing on the platform.
More surprisingly, the H-type seller can also benefit
from Amazon’s threat of entry; this happens if ƒH is
not too large. With no entry threat, the H-type’s firstperiod service is higher because he need not mask
his demand, but Amazon’s fee is also higher because
it now has incentives to raise the fee to benefit from
the H-type’s high demand. In contrast, when Amazon
retains an entry option, the H-type will lose out on
unit sales in the first period as he mimics the L-type
to prevent Amazon’s entry. However, all other factors
benefit him, including a lower fee for both periods
and a lower service cost in the first period. Intuitively,
if ƒH is not too large relative to ƒL , the H-type seller’s
forgone profit in the first period as a result of his
767
strategic reduction of sales will be more than compensated for by the gain in the second-period profit from
his high sales at lowered fees. If ƒH is very high, however, then the H -type seller’s lost unit sales in the first
period will dominate, yielding a lower overall profit
than if Amazon commits to no entry.
Proposition 4. If ˆ < ˆ ∗ , the platform owner’s threat
of entry increases the second-period consumer surplus.
Furthermore, it increases the first-period consumer surplus
in the case of an L-type seller and decreases the first-period
consumer surplus in the case of an H-type seller.
Proposition 4 shows the effect of Amazon’s threat
of entry on the overall consumer surplus when the
probability of an H-type is relatively low (in the pooling parameter region). The consumer surplus in the
second period is clearly higher when Amazon keeps
its entry option than not. This is because in the second period, both types of sellers choose their firstbest service levels and prices given Amazon’s fee (as
in the case of no entry threat), and this fee is lower
when Amazon retains its entry option, which leads
to lower prices to the consumer. For the same reason, in the case of an L-type seller, the first-period
consumer surplus is also higher when Amazon keeps
its entry option. Interestingly, however, in the case
of an H-type seller, the first-period consumer surplus
is actually lower with Amazon’s threat of entry than
without it (in the pooling parameter region). This is
because even though Amazon’s entry option leads to
a lower price, it induces the H-type seller to provide
a significantly lower service level in the first period
to reduce his sales to that of an L-type. That is, in
the first period, because of the H-type seller’s lowered services, significantly fewer consumers will buy
from him than if Amazon had committed to no entry,
in which case the H-type seller would provide a high
service level to benefit from his full demand potential. The net effect is that in the case of an H-type
seller, Amazon’s threat of entry reduces the firstperiod consumer surplus as a result of the H-type
seller’s reduced services to mask his demand.
Proposition 5. (a) The steeper the demand curve (the
larger b), the lower the platform owner’s fee.
(b) The platform owner’s fee increases with ˆ when
ˆ < ˆ ∗ and is independent of ˆ when ˆ > ˆ ∗ .
We obtain the intuitive result that a steeper (i.e.,
more elastic) demand leads to a lower fee by Amazon.
A more elastic demand intuitively means that for
any given decrease in the price to the consumer, the
quantity demanded will increase more. Thus, when
demand is more elastic, Amazon tends to have more
incentive to reduce its fee so as to get the seller to
reduce his prices to sell many more units, which will
768
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Marketing Science 30(5), pp. 757–775, © 2011 INFORMS
lead to higher total fees. We find that Amazon’s pooling equilibrium fee increases as the probability of the
seller being an H-type increases. However, as this
probability becomes large enough, Amazon will effectively be targeting only the H-type seller (to obtain
the separating outcome), and its fee is thereby set
optimally conditional on the seller being an H-type.
Therefore, for large ˆ Amazon’s fee will become constant. In the low-probability event of an L-type seller,
Amazon makes zero profit, but its expected profit is
maximized with the high fee, which induces a separating equilibrium.
Figure 3
Effect of Reviews on Amazon’s Fee
*
fsep
f*
*
frev
*
fpool
0
5.
Effect of Consumer Reviews
Although Amazon may not directly observe the
seller’s service level, it can solicit reviews from the
seller’s first-period customers (because Amazon has
their contact information). Such reviews can, to some
extent, help Amazon estimate the seller’s service
level. Once Amazon knows the service level, it will
be able to better infer the inherent product demand.15
Here, we assume the extreme case that consumer
reviews fully reveal the seller’s service level. After
the first period, Amazon will acquire such reviews
to determine the seller’s service level and hence
correctly infer the seller’s type. Note that the fully
revealing reviews do not imply a full (complete)
information game, because Amazon will know the
seller’s type only after the first period.
Because the seller knows that consumer reviews
will reveal his service level and allow Amazon to
learn his type, he no longer has any incentive to
deviate from his first-best service and price levels
as given in (A3) and (A5). After the first period,
Amazon will learn the seller’s true type via his
reviews and will directly sell the product if the
H-type seller is revealed. In the case of an L-type
seller, Amazon will let him continue in the second period. Given Amazon’s fee frev , both types
of sellers will choose et∗ = 1/42bk5 and pt∗ 4frev 5 =
4ƒt + b4c + frev 5 + 3/44bk55/42b5, which yields a first∗415
period profit of çt = 6ƒ − b4c + frev 5 + 1/44bk572 /44b5.
In the case of an H -type seller, Amazon’s firstperiod profit is frev · 4ƒH − b4c + frev 5 + 1/44bk55/2.
In the second period, Amazon will sell the
product directly, making a maximum profit of
4ƒH − bc + 1/44bk552 /44b5 − F at the optimal price
of pA∗ = 4ƒH + bc + 3/44bk55/42b5. With the L-type
seller, Amazon makes the same profit of frev ·
15
To some extent, Amazon may also use product reviews to infer
the demand. Thus, in our model, such product reviews serve a
similar role to seller reviews in that they help Amazon learn the
seller’s type after the first period.
*
4ƒL − b4c + frev 5 + 1/44bk55/2 for each period. Therefore, Amazon’s expected total profit for both periods
is given by16
ƒ −b4c +frev 5+1/44bk5
çA1rev 4frev 5 = ˆ frev · H
2
4ƒ −bc +1/44bk552
+ H
−F
4b
+241−ˆ5frev
ƒL −b4c +frev 5+1/44bk5
0
2
It is straightforward to show that Amazon’s optimal
fee and profit, respectively, are given by
∗
frev
=
ˆ4ƒH −bc +1/44bk55+241−ˆ54ƒ L −bc +1/44bk55
2b42−ˆ5
and
ç∗A1 rev
=
6ˆ4ƒH − bc + 1/44bk55 + 241 − ˆ54ƒL − bc + 1/44bk5572
8b42 − ˆ5
4ƒH − bc + 1/44bk552
+ˆ
−F 0
4b
Proposition 6. With fully revealing consumer
reviews, the platform owner’s fee is higher when ˆ < ˆ ∗
and lower when ˆ > ˆ ∗ (compared with the case of no
reviews).
Proposition 6, illustrated in Figure 3, shows that
with fully revealing reviews, Amazon’s fee will be
higher when ˆ is small (i.e., in the pooling parameter
region) and lower when ˆ is large (i.e., in the separating parameter region). Recall that without reviews,
if ˆ is small, Amazon has an incentive to lower its
fee from the no-entry-threat level because the H-type
16
We have assumed that ˆ < 424ƒL − bc + 1/44bk555/4ƒH − bc +
1/44bk55; i.e., ˆ is small enough such that both types of sellers will
be targeted by Amazon. Otherwise, Amazon’s optimal decision will
be to completely ignore the possibility of the L-type seller.
Jiang, Jerath, and Srinivasan: Firm Strategies in the “Mid Tail” of Platform-Based Retailing
Marketing Science 30(5), pp. 757–775, © 2011 INFORMS
seller will mimic the L-type in the first period. With
fully revealing reviews, the H-type will not be able
to mask his demand and will thus choose his firstbest service and price levels and sell a high volume in the first period, which gives Amazon the
incentive to charge a higher fee. In contrast, if ˆ is
large (in the separating equilibrium) and there are no
reviews, Amazon loses the potential profit from the
L-type seller. With fully revealing reviews, Amazon
no longer needs to set its fee high to separate the two
types of sellers because reviews will reveal the seller’s
true type. Thus, Amazon will optimally reduce its fee
to capture some profits from the L-type seller.
Not surprisingly, reviews make the H -type seller
worse off because he will make zero profit in the
second period when Amazon enters the market. If
ˆ is small, consumer reviews will also reduce the
L-type seller’s profit because of Amazon’s increased
fee. However, when ˆ is large, consumer reviews
will make the L-type seller better off because Amazon’s reduced fee now allows him to sell profitably
(whereas without reviews he will not be able to sell
profitably). Amazon’s incentive to acquire consumer
reviews can be represented by its potential gain in
profit, which is given by ç∗A1 rev − ç∗A . We find that
in the pooling parameter region, the larger ˆ is, the
more incentive Amazon has to invest in reviews. In
contrast, in the separating parameter region, Amazon
already learns the seller’s type with its optimal high
fee; its expected profit gain from reviews comes from
the L-type seller, whose likelihood decreases as ˆ
increases. Hence, in the high ˆ range, Amazon’s
incentive to acquire reviews will decrease with ˆ.
6.
Robustness to Alternative
Assumptions
In this section, we discuss the robustness of our
insights to several alternative modeling assumptions.
First, our model has focused on the uncertainty in the
demand intercept (ƒ5. Alternatively, the uncertainty
in demand may come from the slope of the demand
curve (b5 rather than the intercept. In such an alternative model, the H-type seller corresponds to the less
elastic demand (i.e., smaller b5, and the L-type seller
corresponds to the more elastic demand (i.e., larger b5.
The analysis for such a model is very similar to the
one that we have done; our key insights remain qualitatively the same.
Second, in practice, platform owners typically
charge sellers a per-unit fee based on the proportion
of their sales price; for example, Amazon’s fee ranges
from 6% to 25% of the sales price depending on the
product category. We have assumed that the per-unit
fee is fixed (not dependent on price). A fee proportional to price will clearly influence the seller’s pricing
769
decisions. However, this does not qualitatively alter
the strategic trade-offs between the platform owner
and the seller, and hence our key results remain qualitatively the same (although the parameter region for
the pooling outcome will be different). In particular, the seller will have more incentives to charge a
lower price because, intuitively, with a proportional
fee, a lower price leads to a lower fee and a lower
overall marginal cost (which has three components:
the wholesale price, the fee paid to Amazon, and the
service cost) to the seller. We find through numerical examples that such intuition is indeed correct.
Because our focus is on the strategic interactions arising from information asymmetric and moral hazard,
rather than on the optimal price per se, using such
a proportional fee only leads to more analytical complexity and does not yield additional insights into our
research questions.
Third, we have assumed the same demand for both
periods. If the product demand varies across periods, we expect our results to qualitatively hold as
long as there is a large enough positive correlation
between the demands across the periods. In particular, if the second-period demand intercept is a multiple  of the first-period demand, then the similar
analysis will carry through—both the platform owner
and the seller need to adjust the demand by the factor
 (which can be larger or small than 1) in the second period. Although the analysis is more complex
with the addition of a new parameter, the strategic
considerations of both the platform owner and the
seller remain qualitatively the same. For example, if
demand falls significantly over time, Amazon will be
more likely to not enter the market or will exit the
market to encourage entry by the third-party sellers.
Fourth, although our model has two time periods,
it can be generalized to any finite number of time
periods. Our main pooling outcome, for example, will
become the following. For a number of initial periods, the H-type seller will mimic the L-type seller;
after that, he will stop mimicking and choose his firstbest service and price for all later periods. In essence,
when there are only a small number of periods left,
the platform owner will no longer find it worthwhile
to enter the market even if it identifies the H-type
seller at that point, because the product will have
reached the later stage of the product life cycle or
because a new version of the product will soon be
released.
Fifth, in our model, we use a pure variable fee
rather than a nonlinear fee that depends on the quantity sold by the seller (perhaps with a quantity discount). A pure variable fee corresponds to reality
in most platform-based retailing settings. However,
our main results regarding the pooling equilibrium
Jiang, Jerath, and Srinivasan: Firm Strategies in the “Mid Tail” of Platform-Based Retailing
770
Marketing Science 30(5), pp. 757–775, © 2011 INFORMS
remain qualitatively the same even if we adopt a nonlinear fee. In the electronic companion, we show that
our focal pooling equilibrium still exists in certain
parameter regions even when a general nonlinear fee
structure is used.
Sixth, we have assumed that Amazon’s fee does not
change across periods. If a dynamic fee is allowed
in our model, Amazon may make more profit without entering the market in the second period after
identifying the high-type seller (and will thus avoid
incurring the entry fee). In theory, after identifying
the high-type seller, Amazon can change its secondperiod fee to extract essentially all the profit from
the seller and thus make more profit than if it enters
the market itself. This separating outcome, though
appearing different, is actually the same from the
high-type seller’s perspective. The high-type seller
makes zero profit in the second period if he is
replaced by Amazon or if Amazon optimally changes
its fee to extract away his entire surplus. In the case
of our focal pooling outcome, allowing for a dynamic
fee in our model will not give Amazon any reason
to change its fee in the second period because Amazon has the same information about the seller’s type
at the beginning of the first and second periods (the
same as the prior probability).
Finally, we have implicitly normalized the seller’s
outside option to have a utility of zero rather than
explicitly modeling any dynamic outside option of the
seller. However, our main intuition and results remain
qualitatively the same if we explicitly introduce a
parameter to represent the seller’s utility for his outside option. Intuitively, we expect that as the seller’s
outside option becomes more attractive, Amazon will
have more incentive to stay out of the market to
attract entry by the sellers who would otherwise not
enter the platform.
7.
Conclusions
As online retailing continues to grow, major retailers such as Amazon.com are relying heavily on the
platform model of selling. Many small independent
sellers utilize the retailing platform to sell products
not carried directly by the platform owner. Platform
retailing is a win–win for all—consumers get easy
access to their preferred but hard-to-find products, the
small companies get access to these consumers, and
the platform owner keeps a percentage of the independent sellers’ revenues. However, anecdotal evidence suggests that there is an interesting dynamic
prevalent in platform retailing. The platform owner
has an incentive to let the independent sellers offer
products on its platform, observe the sales of these
products, and then cherry-pick the products with high
sales potential to procure and sell directly, effectively
driving the independent seller’s sales to zero. Anticipating the platform owner’s demand-learning and
cherry-picking incentives, the independent seller has
an incentive to hide any high demand by strategically lowering his services to reduce his early sales
to prevent the platform owner from learning the true
demand. The platform owner, in turn, needs to decide
how to set its fee knowing that a high-demand seller
has an incentive to mask his demand.
As an outcome of these strategic interactions, we
find that even though the platform owner can set a
high enough fee to identify the high-demand seller, it
may not always be optimal to do so. If the probability of the seller being an H-type is relatively low, the
platform owner will charge a low fee such that both
types of sellers sell on the platform. This results in a
pooling equilibrium in which the platform owner is
unable to learn the true demand because the H-type
seller can mask his demand by under-investing in services. Because of this inefficiency, the platform owner
is, surprisingly, worse off by keeping its option of
entry. Furthermore, the platform owner’s threat of
entry may benefit both types of sellers because they
have to pay a lower fee, although it may reduce or
increase the consumer surplus.
Service standardization and monitoring by the platform owner tend to reduce but not completely remove
the H-type seller’s ability to use reduced services or
efforts to mask his demand. The platform owner can
also invest in acquiring consumer reviews. With fully
revealing consumer reviews, the platform owner will
be able to learn the true demand after the initial time
period. We find that such consumer reviews benefit
the platform owner and will hurt both types of sellers
in the pooling parameter region (with a low ex ante
probability of the seller being an H-type). However,
even good consumer reviews are unlikely to fully
reveal the seller’s service level, because such reviews
tend to reveal postsale service levels rather than presale services. If there is mediocre presale service, some
consumers may not buy the product and hence cannot write seller reviews as is the case on Amazon.
Thus, to the extent that consumer reviews may not
fully reveal the seller’s service level, the H-type seller
may still be able to strategically mask his demand.
Interestingly, our framework can be reinterpreted
to provide insights into nonplatform retailing situations as well. Suppose that a manufacturer introduces
a new product in a certain market. The manufacturer
is not certain whether the product will have a high
demand (ƒH 5 or a low demand (ƒL 5, but it knows
the product has a prior probability of ˆ for the high
demand. The manufacturer may sell through a local
retailer who can privately observe the demand potential (ƒH or ƒL 5 and decide how much promotional
Jiang, Jerath, and Srinivasan: Firm Strategies in the “Mid Tail” of Platform-Based Retailing
771
Marketing Science 30(5), pp. 757–775, © 2011 INFORMS
effort (e5 to invest. The manufacturer collects a wholesale price (f 5 from the local retailer but has incentives
to go direct if it learns the product demand is high
but not if the demand is low. Such a setting is isomorphic to our model. Our analysis suggests that unless
the manufacturer has a high enough prior for a hit
product, it should commit to the local retailer that it
will not go direct.
Our study is the first to explore the strategic
interactions between the platform owner and the
independent sellers in the mid tail of online platformbased retailing, and it offers several avenues for
future research. For instance, motivated by the actual
contract structure on Amazon, we have assumed a
single per-unit fee contract. With hundreds of thousands of independent sellers, even if the platform
owner uses a menu with several options to distinguish between different sellers and classify them, our
analysis will be relevant for the thousands of independent sellers within each class. Nevertheless, extending
our framework to a menu of contracts may yield interesting insights with regard to separating outcomes.
We analyze a case with one third-party seller (of
either type H or L) and a monopoly platform owner.
However, there could be competition at both levels.
If multiple sellers on the platform sell the same product, there can still be a symmetric pooling equilibrium in which all sellers prefer to mask the high
demand. However, the incentive for each seller to
mask the high demand will reduce because of possible free riding from other sellers. As the number of
sellers increases, we expect that the free-riding problem will become more severe and that the symmetric pooling outcome may become less likely to be the
realized equilibrium outcome. If we introduce competing platforms in our model, our main results and
intuitions will hold as long as each platform has a
segment of loyal online consumers. Furthermore, with
competing platforms, the unit fees charged by the
platform owners will tend to be lower because of
competition. With lower fees, it is more likely that
sellers of all demand types will enter the platforms.
Hence, intuitively, we expect that the existence of
competing platforms will make the pooling outcome
(our focal equilibrium) even more likely to occur. In
practice, Amazon has become by far the most dominant retail platform with substantial monopoly power
(because of its already established two-sided network). Even its rival platform Buy.com has begun selling as a third-party seller on Amazon. Future research
may explicitly study, both empirically and analytically, the competition between competing platforms
such as Amazon with eBay or Sears.com, or Apple’s
App Store with Google’s Android Market.
8.
Electronic Companion
An electronic companion to this paper is available as
part of the online version that can be found at http://
mktsci.pubs.informs.org/.
Acknowledgments
This paper is based on the second essay of B. Jiang’s
doctoral dissertation at Carnegie Mellon University. The
authors are grateful to Nitin Mehta for extensive discussions
that have tremendously improved this paper. The authors
also thank seminar participants at the Rotman School of
Management at the University of Toronto, the Ross School
of Business at the University of Michigan, the Olin Business School at Washington University in St. Louis, INSEAD,
Tsinghua University, Peking University, and the editor, area
editor, and two anonymous reviewers.
Appendix
Proof of Lemma 1. Without threat of entry from
Amazon, the seller’s optimal prices and service levels
should be the same across the two periods because Amazon’s fee f¯ does not change across periods. The seller
4i5
4i5
chooses his service level (ēt ≥ 05 and price (p̄t ≥ 05 to maximize his profit for each period i:
4i5
4i5
4i5
4i5
4i5
ç̄t = 4ƒt + ēt − b p̄t 56p̄t − c − f¯ − k4ēt 52 70
The first-order conditions (FOCs) are
4i5
¡ ç̄t
4i5
¡ p̄t
4i5
4i5
4i5
4i5 = 4ƒt + ēt −b p̄t 5−b p̄t −c − f¯ −k4ēt 52 = 01
(2)
4i5
¡ ç̄t
4i5
¡ ēt
4i5
4i5
4i5
4i5
4i5 = 4ƒt + ēt −b p̄t 5·4−2kēt 5+ p̄t −c − f¯ −k4ēt 52 = 00
(3)
4i5
p̄t
4i5
4ƒt + ēt
4i5
+ b4c + f¯ + k4ēt 52 55/42b5.
4i5
solve for ēt :
From (2), we obtain
=
Substituting this into (3), we then
4i5
1 ¡ ç̄t
4i5
4i5
4i5
=
k
ē
bk4ēt 52 − ēt − 6ƒt − b4c + f¯57 = 00
−
t
4i5
2bk
¡ ēt
Thus, the potential FOC solutions are
∗4i5
ēt
1
∗4i5
1
ēt =
2bk
q
1 ± 1 + 4bk6ƒt − b4c + f¯57
(4)
0
(5)
2bk
We eliminate (5) since simple algebra shows that it yields
∗4i5
4i5
∗4i5
zero demand: q̄t 4f¯5 = ƒt + ēt − b p̄t = 00
Alternatively, one can formally apply the second partial
derivative test (using the Hessian matrix) to show that (4)
is the local maximum and (5) is a saddle point. It is easy
4i5
4i5
to show that the boundary of ēt = 0 and p̄t = 0 yields a
lower profit than (4). Hence, (4) is the seller’s (global) profitmaximizing service level, with the corresponding optimal
price and profit respectively given by (6) and (7) below:
=
ƒ + b4c + f¯5 + 3/44bk5
∗4i5
p̄t 4f¯5 = t
1
2b
6ƒ − b4c + f¯5 + 1/44bk572
∗415
∗425
ç̄∗t 4f¯5 = ç̄t + ç̄t = t
0
2b
Lemma 1 immediately follows. ƒ
(6)
(7)
Jiang, Jerath, and Srinivasan: Firm Strategies in the “Mid Tail” of Platform-Based Retailing
772
Marketing Science 30(5), pp. 757–775, © 2011 INFORMS
Equilibrium Outcome When Amazon Commits to
No Entry (§4.2)
The optimal service levels, prices, and overall profit
for a seller of type t are given by (4), (6), and (7),
respectively. Amazon’s expected total profit is given by
P
4i5
4i5
4i5
ç̄A 4f¯5 = 2i=1 8f¯6ˆ q̄H 4f¯5 + 41 − ˆ5q̄L 4f¯579, where q̄t 4f¯5 =
∗4i5
∗4i5
ƒt + ēt − b p̄t 4f¯5 is type t ∈ 8L1 H9 seller’s quantity sold
in period i as a function of f¯. Substitution of (4) and (6)
4i5
into q̄t 4f¯5 leads to ç̄A 4f¯5 = f¯6ˆƒH + 41 − ˆ5ƒL − b4c + f¯5 +
1/44bk57. Amazon’s equilibrium fee and profit are17
ˆƒ + 41 − ˆ5ƒL − bc + 1/44bk5
1
f¯∗ = H
2b
6ˆƒH + 41 − ˆ5ƒL − bc + 1/44bk572
ç̄∗A =
0
4b
(8)
(9)
Substituting (8) into (6) and (7), we obtain the equilibrium
outcome for type t ∈ 8L1 H9 seller:
∗415
p̄t
2ƒ t + ˆƒH + 41 − ˆ5ƒL + bc + 7/44bk5
1
4b
62ƒt − ˆƒH − 41 − ˆ5ƒL − bc + 1/44bk572
ç̄∗t =
0
8b
∗425
= p̄t
=
(10)
(11)
Separating Outcome
Amazon’s expected profit is expressed as
çA1 sep 4fsep 1 eA 1 pA 5 = ˆfsep ·
ƒH − b4c + fsep 5 + 1/44bk5
2
+ ˆ64pA − c − keA2 54ƒH + eA − bpA 5 − F 70
A proof very similar to that for Lemma 1 shows that eA∗ =
1/42bk5 and pA∗ = 4ƒH + bc + 3/44bk55/42b5 (because of space
considerations, we exclude it from this paper). With this,
we can rewrite Amazon’s expected profit as a function of
only fsep , where, as discussed before, 4ƒL − bc + 1/44bk55/b ≤
fsep < 4ƒH − bc + 1/44bk55/b:
ƒH − b4c + fsep 5 + 1/44bk5
çA1 sep 4fsep 5 = ˆfsep ·
2
4ƒH − bc + 1/44bk552
+ˆ
−F 0
4b
After we fully specify Amazon’s expected profit for all
fee intervals, we then determine which fee maximizes
Amazon’s expected profit and hence which type of equilibrium is realized. Note that by maximizing (12), if a separating equilibrium is realized, Amazon’s fee must be given
by (13), its expected profit by (14), and the seller’s profit
by (15) and (16). The two forms in (13)–(15) are according to
whether the maximum occurs at an interior point or at the
boundary. Later, we specify in Proposition 1 the condition
under which this equilibrium is realized.

1
ƒ − bc + 1/44bk5

 L
1 if ƒH < 2ƒL − bc +
1

b
4bk
∗
(13)
fsep
=


 ƒH − bc + 1/44bk5 1 if ƒ ≥ 2ƒ − bc + 1 3
H
L
2b
4bk
∗
çA1 sep
 4ƒL −bc +1/44bk554ƒH −ƒL 5 4ƒH −bc +1/44bk552


+
−F
1
ˆ


2b
4b



1



 if ƒH < 2ƒL −bc + 4bk
= (14)


34ƒH −bc +1/44bk552


ˆ
−F 1



8b



1
 if ƒ ≥ 2ƒ −bc +
3
H
L
4bk

2
1

 4ƒH −ƒL 5 1

if ƒH < 2ƒL −bc +
1

4b
4bk
∗
çH1 sep =
(15)

 4ƒH −bc +1/44bk552
1


1 if ƒH ≥ 2ƒL −bc +
3
16b
4bk
ç∗L1 sep = 00
(16)
Pooling Outcome
For the sake of clarity and completeness, we list below the
seller’s pooling equilibrium decisions (as indicated by the
subscript “pool”) for both periods with (17) and (18) for
the L-type seller and (19)–(22) for the H -type seller:
1
1
(17)
2bk
ƒ + b4c + f 5 + 3/44bk5
∗415
∗425
pL1 pool = pL1 pool = L
1
(18)
2b
1
∗415
eH1 pool = ƒL +
− ƒH 1
(19)
2bk
ƒ + b4c + f 5 + 3/44bk5
∗415
pH1 pool = L
1
(20)
2b
1
∗425
eH1 pool =
1
(21)
2bk
ƒ + b4c + f 5 + 3/44bk5
∗425
pH1 pool = H
0
(22)
2b
From these, we can easily compute the overall profit for
each type of seller as a function of f :
∗415
∗425
eL1 pool = eL1 pool =
(12)
Recall that Assumption C1(ii) implies that if Amazon
knows that the seller is an H -type, it will enter the market in the second period, because doing so yields a profit
of 4ƒH − bc + 1/44bk552 /44b5 − F rather than the maximum
potential profit of 4ƒH − bc + 1/44bk552 /48b5 from the fee collected from the H-type. At this point, we cannot yet fully
determine whether or not a separating equilibrium will be
realized for the overall game, because we must also calculate Amazon’s profit for any fee f < 4ƒL − bc + 1/44bk55/b.
17
Here, we have implicitly assumed a nonboundary solution.
That is, ˆ and ƒH are not both so large that Amazon will totally
ignore the possibility of an L-type seller and target only the H -type
seller (by charging f ∗ = 4ƒH − bc + 1/44bk55/42b55. One can easily
show that such a boundary solution requires both
2
ƒL − bc + 1/44bk5
1
ˆ>
and ƒH > 2ƒL − bc +
0
ƒH − ƒL
4bk
ç∗L1 pool 4f 5 =
∗415
6ƒL −b4c +f 5+1/44bk572
1
2b
(23)
∗425
ç∗H1 pool 4f 5 = çH1 pool 4f 5+çH1 pool 4f 5
∗415
∗415
2
∗415
∗415
= 6pH1 pool −c −f −k4eH1 pool 5 74ƒH +eH1 pool −bpH 1 pool 5
+
6ƒH −b4c +f 5+1/44bk572
0
4b
(24)
Jiang, Jerath, and Srinivasan: Firm Strategies in the “Mid Tail” of Platform-Based Retailing
773
Marketing Science 30(5), pp. 757–775, © 2011 INFORMS
Amazon’s expected total profit is given by çA1 pool 4f 5 =
415
425
çA1 pool 4f 5+çA1 pool 4f 5. It chooses f to maximize its expected
profit. Amazon’s optimal pooling fee and profit are given
by18
ˆ4ƒH − ƒL 5/2 + ƒL − bc + 1/44bk5
1
(25)
2b
6ˆ4ƒH − ƒL 5/2 + ƒL − bc + 1/44bk572
ç∗A1 pool =
0
(26)
4b
Proof of Proposition 1. Note that Amazon dictates
which equilibrium is realized by selecting the appropriate
fee f . Thus, for any given set of parameter values, we simply need to compare Amazon’s expected profits under the
two types of equilibria (in two different fee intervals) to
determine the realized equilibrium for the overall game. For
any given set of parameter values, we obtain a separating
equilibrium if ç∗A1 sep ≥ ç∗A1 pool and a pooling equilibrium if
ç∗A1 sep < ç∗A1 pool .
Figure A.1
Amazon’s Pooling and Separating Profits
ΠA,* sep
∗
fpool
=
Case 1. ƒH ≥ 2ƒ L − bc + 1/44bk5.
We examine two subcases. First, we consider the condition of
24ƒL − bc + 1/44bk55
0
ˆ>
ƒH − ƒL
As discussed before, a pooling equilibrium requires f <
4ƒL − bc + 1/44bk55/b such that the L-type will profitably sell
a positive quantity. However, if
ΠA,* pool
ˆ>
ˆ
çA1 pool 4f 5 →
ˆ4ƒH − ƒL 56ƒL − bc + 1/44bk57
0
2b
From (14) and assumption C1(ii), we get
ç∗A1 sep
34ƒH −bc +1/44bk552
ˆ4ƒH −bc +1/44bk552
=ˆ
−F >
8b
4b
>
ˆ4ƒH −ƒL 56ƒL −bc +1/44bk57
0
2b
Note that the last inequality is proved by expanding the
terms:
ˆ4ƒH − bc + 1/44bk552 ˆ4ƒH − ƒL 56ƒL − bc + 1/44bk57
>
4b
2b
⇔ 4ƒH − ƒL 52 − 4ƒL − bc + 1/44bk552 > 0
1
⇔ ƒH − ƒL > ƒL − bc +
1
4bk
18
In the proof of Proposition 1, we show that Amazon’s pooling
profit at the boundary f → 4ƒL − bc + 1/44bk55/b is always lower
than its separating profit. Hence, (27) is the only possible pooling
equilibrium fee.
24ƒL − bc + 1/44bk55
0
ƒH − ƒL
34ƒH − bc + 1/44bk552
−F
8b
−
implies that Amazon’s best pooling outcome corresponds to
a fee f → 4ƒL − bc + 1/44bk55/b. As → 4ƒL − bc + 1/44bk55/b,
Second, we consider the condition of ˆ ≤ 24ƒL − bc +
1/44bk55/4ƒH − ƒL 5, which means that the best pooling outcome occurs at the FOC point (25). We compare Amazon’s
profits from the potential separating equilibrium (14) and
the potential pooling equilibrium (26). The separating equilibrium is realized if and only if ç∗A1 sep ≥ ç∗A1 pool or
the FOC solution
ˆ4ƒH − ƒL 5/2 + ƒL − bc + 1/44bk5 ƒL − bc + 1/44bk5
>
2b
b
1
which is true under Case 1. Thus, we conclude that the
separating equilibrium is realized if
24ƒL − bc + 1/44bk5
ˆ>
1
ƒH − ƒL
∗
fpool
=
*
0
6ˆ4ƒH − ƒL 5/2+ƒ L − bc + 1/44bk572
≥ 00
4b
We plot both ç∗A1 sep and ç∗A1 pool as a function of ˆ in Figure A.1. These two curves (one linear and one quadratic
in ˆ5 have two points of intersection with one intersection
on each side of ˆ = 1, because
lim8ç∗A1 sep −ç∗A1 pool 9
ˆ→1
64ƒH −ƒL 5/2+ƒL −bc +1/44bk572
34ƒH −bc +1/44bk552
=
−F −
8b
4b
2
1
ƒ +ƒL
1 2
1
3 ƒH −bc +
−2 H
−bc +
−8bF
=
8b
4bk
2
4bk
2
1
1
ƒ +ƒL
1 2
>
3 ƒH −bc +
−2 H
−bc +
8b
4bk
2
4bk
2
4ƒ −bc +144bk55
−8b H
(from assumption C1(ii))
8b
1
1 2
ƒH +ƒL
1 2
=
ƒH −bc +
−
−bc +
> 00
4b
4bk
2
4bk
Thus, if ˆ ≥ ˆ ∗ , the separating equilibrium will be realized;
if ˆ < ˆ ∗ , the pooling equilibrium is realized, where ˆ ∗ , the
smaller root of
34ƒH − bc + 1/44bk552
ˆ
−F
8b
=
6ˆ4ƒH − ƒL 5/2+ƒ L − bc + 1/44bk572
1
4b
Jiang, Jerath, and Srinivasan: Firm Strategies in the “Mid Tail” of Platform-Based Retailing
774
Marketing Science 30(5), pp. 757–775, © 2011 INFORMS
is given by
Using Equations (8) and (25), one can then easily show that
415
∗
¯ 415 4f¯∗ 5. ƒ
CSH 4fpool
5 < CS
H
ˆ ∗ = 434ƒH − bc + 1/44bk552 − 8bF − 24ƒH − ƒL 5
· 4ƒL − bc + 1/44bk55 − 4634ƒH − bc + 1/44bk552 − 8bF
2
2
− 24ƒH − ƒL 54ƒL − bc + 1/44bk557 − 44ƒH − ƒL 5
· 4ƒH − bc + 1/44bk552 51/2 5 · 4ƒH − ƒL 5−2 0
Proof of Proposition 5. This follows immediately from
(25) and (13).
Proof of Proposition 6.
Case 2. ƒH < 2ƒ L − bc + 1/44bk5.
The separating equilibrium is realized if and only if
ç∗A1 sep ≥ ç∗A1 pool or
4ƒL + 1/44bk5 − bc54ƒH − ƒL 5 4ƒH − bc + 1/44bk552
+
−F
ˆ
2b
4b
6ˆ4ƒH − ƒL 5/2+ƒ L − bc + 1/44bk572
≥ 00
4b
Thus, if ˆ ≥ ˆ ∗ , the separating equilibrium will be realized;
if ˆ < ˆ ∗ , the pooling equilibrium is realized, where
−
ˆ ∗ = 424ƒH − bc + 1/44bk552 − 8bF + 24ƒH − ƒL 5
2
· 4ƒL − bc + 1/44bk55 − 4624ƒH − bc + 1/44bk55 − 8bF
+ 24ƒH − ƒL 54ƒL − bc + 1/44bk5572 − 44ƒH − ƒL 52
· 4ƒH − bc + 1/44bk552 51/2 5 · 4ƒH − ƒL 5−2 0
∗
∗
frev
−fpool
=
ˆ4ƒH −bc +1/44bk55+241−ˆ54ƒ L −bc +1/44bk55
2b42−ˆ5
ˆ4ƒH −ƒL 5/2+ƒ L −bc +1/44bk5
2b
2
ˆ 4ƒH −ƒL 5
=
> 00
4b42−ˆ5
−
If ƒH < 2ƒL − bc − 1/4bk,
∗
∗
frev
−fsep
=
ˆ4ƒH −bc +1/44bk55+241−ˆ54ƒ L −bc +1/44bk55
2b42−ˆ5
ƒL −bc +1/44bk5
b
1
× 4ˆ4ƒH −bc +1/44bk55
=
2b42−ˆ5
−
ƒ
+241−ˆ54ƒL −bc +1/44bk55
∗
Proof of Proposition 2. We define ˆ to be the cutoff
constant given in Proposition 1. Hence, if Amazon keeps its
entry option and ˆ < ˆ ∗ , the pooling equilibrium outcome
will be realized. Comparing (8) and (25), it is simple to show
∗
∗
fpool
< f¯ . Comparing Amazon’s pooling equilibrium profit
given by (26) with its no-threat-of-entry profit given by (9),
one easily shows that ç∗A1 pool < ç̄∗A . ƒ
Proof of Proposition 3. Please refer to the electronic
companion for the proof.
Proof of Proposition 4. Computing consumer surplus
(CS) from an inverse linear demand function is straightforward. The second-period consumer surplus depends on the
seller’s type. From Equations (4) and (6) and the demand
function, one easily shows that without Amazon’s threat of
entry, the consumer surplus in each period for the t-type
seller is given by
6ƒt − b4c + f¯∗ 5 + 1/44bk572
0
8b
When Amazon keeps its entry option, the pooling equilibrium is realized if ˆ < ˆ ∗ ; the second-period consumer surplus is
415
=
425
∗
CSt 4fpool
5=
∗
6ƒt − b4c + fpool
5 + 1/44bk572
∗
8b
0
∗
∗
Since fpool
< f¯ , we conclude CSt 4fpool
5 > CSt 4f¯∗ 5.
415
∗
¯ 415 4f¯∗ 5 obviously
For the first period, CSL 4fpool
5 > CS
L
holds because in the first period, the L-type seller chooses
the same first-best price and service level as in the second
period. Under the threat of entry, the pooling consumer surplus in the first period is exactly the same for both types of
sellers, because the H -type exactly mimics the L-type. Thus,
415
∗
∗
CSH 4fpool
5 = CSL 4fpool
5=
∗
6ƒL − b4c + fpool
5 + 1/44bk572
8b
ˆ4ƒH −bc +1/44bk55−24ƒL −bc +1/44bk55
< 00
2b42−ˆ5
∗
∗
frev
−fsep
=
ˆ4ƒH −bc +1/44bk55+241−ˆ54ƒ L −bc +1/44bk55
2b42−ˆ5
ƒH −bc +1/44bk5
2b
1
=
× 4ˆ4ƒH −bc +1/44bk55
2b42−ˆ5
−
+241−ˆ54ƒL −bc +1/44bk55
−42−ˆ54ƒH −bc +1/44bk55
=
41−ˆ54ƒL −ƒH 5
< 00
b42−ˆ5
Here, we have implicitly assumed the interesting case of
ˆ < 24ƒL − bc + 1/44bk55/4ƒH − bc + 1/44bk55 such that both
types of sellers are targeted by Amazon. ƒ
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425
If ƒH ≥ 2ƒL − bc − 1/4bk,
425
CSt 4f¯∗ 5 = CSt 4f¯∗ 5 =
415
−242−ˆ54ƒL −bc +1/44bk555
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